The Quadratic Formula

And the discriminant

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ solves every quadratic.
• Discriminant $\Delta = b^2 - 4ac$: positive means 2 roots, zero means 1, negative means none (real).
• Check your roots by substituting them back.

Steps

1. One formula for every quadratic
2. The discriminant
3. Use the formula
4. Just touching
5. The golden ratio
6. How many roots?